1. Field of the Invention
The present invention generally relates to a method for estimating thermal displacement of a component of a machine tool by using an experimentally obtained expression.
2. Description of the Prior Art
Generally, due to its mechanical nature, a machine tool has several heat sources, such as the roller bearings of the main shaft. Heat generated from such sources is conducted to other components of the machine tool, causing thermal displacement of mechanical components. Generally, when the thermal displacement is in a steady state, for example, when the rotational speed of the main shaft is constant, the following expression accurately accounts for the proportional relationship between the thermal displacement of the main shaft and the difference in temperature between the main shaft and the bed: EQU Thermal displacement=K.times.temperature difference (1)
where K=coefficient.
Since such thermal displacement greatly affects the accuracy of machining, various methods for estimating and/or compensating for this thermal displacement in a machine tool have been proposed. One conventional method is to cool the heat sources. Another is to estimate the thermal displacement based on the temperature of a machine tool and then to compensate for its thermal displacement.
An example of the latter method is disclosed in Japanese Published Examined Patent Application No. S61-59860. This particular method attempts to estimate the thermal displacement of the main shaft by using an experimentally obtained and memory-stored expression representing the relationship between the displacement and the temperature difference between the main shaft head and of the body of a machine tool, which is subjected to relatively small temperature fluctuations. This method includes the steps of (1) measuring the temperatures of the main shaft head and of the body of a machine tool, which is subjected to relatively small temperature fluctuations, based on outputs of two sensors attached to these two components and (2) estimating the thermal displacement of the main shaft based on the difference between the instantaneous outputs of the two sensors. Subsequently, compensation corresponding to the estimated displacement is made by a servomechanism.
Japanese Published Examined Patent Application No. H6-22779 discloses another method that estimates the thermal displacement of the main shaft in the axial direction of a machine tool by using experimentally obtained expressions for the thermal displacement of different elements of the main shaft.
However, because these conventional methods use instantaneous values representative of detected temperatures, they cannot compensate for the delays caused by the time constant of the temperature change and the time constant of the thermal displacement. Therefore, an estimation error tends to occur when the thermal displacement is in a transient state following a change in the rotational speed of a rotatable component, such as the main shaft. Furthermore, these methods do not take into account a change in the rotational speed of the main shaft when thermal displacement is already in a transient state. Nor do they take into account the fact that the time constants can change as a function of the rotational speed of the main shaft. For these reasons, these known methods fail to accurately estimate thermal displacement under all operational conditions of a machine tool.
To illustrate the foregoing, an experiment was conducted to determine the accuracy of the conventional method following a change in the rotational speed of a rotatable component. FIG. 1A is a graph showing changes made in the rotational speed of the main shaft of a machining center in this experiment. The graph of FIG. 1B shows the relationship between the thermal displacement of the main shaft and the fluctuations in the temperature of the main shaft (relative temperature difference between the main shaft and the body of a machine tool) in this experiment. The thermal displacement of the main shaft was estimated by the conventional method using the instantaneous values for the temperature difference in the following expression: EQU Thermal displacement .delta.=5.times.(temperature difference+0.8).(2)
FIG. 1C is a graph showing the estimated error of the thermal displacement estimated by the conventional method when compared to the actual thermal displacement.
The error fluctuations indicate that the error is significant in the transient state following each change from a high rotational speed to a low rotational speed and that it is increasingly more pronounced as the amount of change in the speed is greater. To further illustrate this drawback inherent in the method that uses the instantaneous values of temperatures, FIGS. 2A and 2B show the measurements of the temperature difference and thermal displacement, respectively, divided by the amount of change for each instance of reduction in the rotational speed (from 20,000 min.sup.-1 to 6,000 min.sup.-1, from 20,000 min.sup.-1 to 2,000 min.sup.-1, etc.). The graph of FIG. 2B includes the curve for the temperature difference for comparison.
It can be clearly seen from these charts that while the curves representing the temperature differences exhibits very similar time constants regardless of the degree of change in the rotational speed, the time constant of the thermal displacement becomes greater as the change in the rotational speed becomes greater. In short, if instantaneous temperature outputs are used to estimate thermal displacement in a transient state, the difference between the time constant of the thermal displacement and that of the temperature results in error in estimate which is more pronounced as the change from a higher speed to a lower rotational speed becomes greater.
Applicant of the present application discloses in Japanese Published Exarnined Patent Application No. H8-30982 (which corresponds to U.S. patent application Ser. No. 08/800,581) novel methods for estimating the thermal displacement of a main shaft of a machine tool in a transient state following a change in the rotational speed until a steady state is restored. This method includes a step of estimating the thermal displacement of a main shaft using an operational expression which includes a time-varying coefficient or a coefficient that changes with the number of compensation operations performed thus far. In this way, since the time response of the temperature change coincides with the time response of the thermal displacement when the thermal displacement is in a transient state, the thermal displacement of the main shaft can be accurately estimated under all operating conditions.
In one embodiment of the above-described method, when the thermal displacement is in a transient state, filtering is performed on the measured temperature data of a target machine tool component, such as the main shaft. Preferably, a digital filter such as an exponential smoothing filter can be used for this purpose. A time-varying function f(n) is used as the filter coefficient. Alternatively, the function f(n) may be a function that changes with the temperature data sampling intervals or with the number of estimation operations performed thus far. Particularly, a tentative value for an estimate of the thermal displacement is given by the following operational expression: EQU Y.sub.n =Y.sub.n-1 +(X.sub.n -Y.sub.n-1).multidot.f(n) (3)
where
X.sub.n =temperature data from nth measurement, PA1 Y.sub.n =nth tentative value for estimation of thermal displacement, PA1 f(n)=filter coefficient, and PA1 n=number of estimation operations (period of time).
In this way, the coefficient is continuously changed to an optimum value so that the difference between the estimated thermal displacement and the thermal displacement model is minimized even when the displacement is in a transient state as shown in FIG. 3. FIG. 4 is a graph showing the filter coefficient function f(n) that changes with time. This embodiment, therefore, can compensate for the difference between the time constant of the temperature and the time constant of the thermal displacement, thus accurately estimating the thermal displacement of a machine tool component under all operating conditions, whether the thermal displacement is in a transient state or in a steady state. It should be noted that if the filter coefficient function f(n) is kept constant as shown in FIG. 5, the same dead time appears in the time response of the estimated thermal displacement as when first order lag system temperature data is input into the first order system. Consequently, an accurate estimate of the thermal displacement cannot be obtained in that case.
The function f(n) is subject to change depending on the time constant of the temperature, Ttmp, and the time constant of the thermal displacement, T .delta.. Furthermore, these time constants are subject to significant change due to many factors. One such factor is that the mechanism for heat generation and heat transfer for a decelerating main shaft differs from that of an accelerating main shaft. Another factor is that heat radiation changes as the rotational speed of the main shaft decreases. FIG. 6 shows the changes with time in the filter coefficient for an increase and decrease in the rotational speed.
In view of the foregoing description, in another embodiment, the filter coefficient starts to change when a change occurs in the rotational speed of the main shaft or when a command to change the rotational speed is issued by a control device. To further enhance the accuracy of estimation, the method disclosed in the Japanese Patent Application monitors the temperature change of the main shaft whenever the rotational speed changes. The method then determines the change in the filter coefficient depending on whether the temperature has risen or fallen. For the purpose of reference, FIG. 7 shows changes with time in the filter coefficient corresponding to decreases in the rotational speed to different lower speeds. According to the last two embodiments, since time constants that change with the rotational speed of the main shaft are reflected in the selection of the filter coefficient, the heat displacement of the main shaft can be more accurately estimated.
If the main shaft is rotated by a built-in motor, heat generated by the motor also affects the thermal displacement significantly. Accordingly, in another embodiment, this method monitors the output of a motor by using a numerical control unit and starts to change the filter coefficient when the output of the motor exceeds a threshold value, thus accurately estimating the thermal displacement of the main shaft caused by heat generated by the built-in motor.
The rotational speed of a machine tool component, such as the main shaft, may change when the thermal displacement is already in a transient state. Both the temperature and the thermal displacement of the component exhibit a first-order lag response to the rotational speed of the component. Therefore as shown in the model of FIG. 8, the thermal displacement can be accurately estimated by expression (3) in a period A in which the displacement is not in a steady state but in a transient state due to a change in the rotational speed. In a period B, following another change in rotational speed, the displacement is in a transient state and the temperature and the thermal displacement decrease. Since in period A the temperature data is higher than the above-described tentative value for estimation in period A, the tentative value in period B is pulled up by the higher temperature and remains higher than the displacement model in period B, thereby causing an estimation error.
In still another embodiment, to eliminate such an estimation error, the estimation method disclosed in the Japanese Patent Application determines whether there is a change in rotational speed while the thermal displacement is in a transient state; determines the gap between the tentative value given by expression (3) and the temperature data preceding the change; and, after the change in rotational speed, estimates the thermal displacement by substituting the most recently sampled temperature data with a gap absorption value added thereto into expression (3). Preferably, the gap absorption value is calculated by including in the calculation a temperature time constant Ttmp and the time "t" elapsed since the change in the rotational speed. The following expressions account for the above processing: EQU Gap=temperature data preceding rotational speed change-tentative value for displacement estimation (4) EQU Temperature data for substitution=current temperature data-gap.multidot.exp(-t/Ttmp) (5)
where "temperature data for substitution" corresponds to X.sub.n in the expression (3), "t" is the elapsed time from a change in the rotational speed, and "Ttmp" is a temperature time constant.
FIG. 9 shows an estimation model to which this gap absorption processing is applied. This estimation model indicates that accurate estimation is performed.
Preferably, optimum filter coefficients may be experimentally obtained for each elapsed time, number of estimation operations, change in rotational speed, and/or command to change the rotational speed of a specific machine tool. In addition, such optimum filter coefficients may be stored in matrix tables in a storage of the numerical control device so that a suitable coefficient is retrievable for a specific machining operation. Alternatively, it will suffice to estimate the thermal displacement of the main shaft of a machine tool by expression (1) using the instantaneous temperature value and applying expressions (3)-(5) to estimation given by expression (1).
However, the above-described methods have certain drawbacks. First, an appropriate coefficient f(n) of the operational expression is difficult to determine because the mechanism for heat generation and heat transfer for a decelerating main shaft differs from that of an accelerating main shaft. Another reason for the difficulty is that the heat radiation differs significantly depending on how much the rotational speed has been decreased.
Secondly, to enhance the accuracy of estimation, a large number of matrix tables of optimum coefficients for the filter corresponding to all conceivable operating conditions of the machine tool are required. This means that a large number of experimental measurements must be performed and that the capacity of the storage device must be increased accordingly. In addition, a great deal of time is required to retrieve an optimum coefficient, which affects the response of the entire system.